Haman’s Sons in Bnei Brak

While ten of Haman’s sons met their fate by hanging – a real “family tree” if there ever was one – the Gemara in Megilla states that he actually had many more sons, maybe even over 200! What became of the rest of his family? The Gemara there fills in some of the details. The Gemara in Sanhedrin (96b) shares one amazing twist: some of Haman’s descendants went on to teach Torah in Bnei Brak. It is poetic justice – Haman’s very own bloodline helped ensure Jewish continuity, even though he tried to wipe it out!
There is a Pesach Seder anecdote about five sages in Bnei Brak who were so engrossed in discussing the Exodus story that they completely lost track of time. Could it be that the same Bnei Brak is where Haman’s descendants, now Torah teachers, made their mark?
First, another issue must be addressed. How could Haman’s descendants convert to Judaism and eventually become esteemed Torah teachers since we have a halachic prohibition against accepting converts from Amalek?